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Improvement of the critical temperature of NbTiN films on III-nitridesubstratesTo cite this article: Houssaine Machhadani et al 2019 Supercond. Sci. Technol. 32 035008

 

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Improvement of the critical temperature ofNbTiN films on III-nitride substrates

Houssaine Machhadani1, Julien Zichi2, Catherine Bougerol3,Stéphane Lequien4, Jean-Luc Thomassin1, Nicolas Mollard4,Anna Mukhtarova1, Val Zwiller2, Jean-Michel Gérard1 and Eva Monroy1

1Univ. Grenoble-Alpes, CEA-INAC-PHELIQS, 17 av. des Martyrs, F-38000 Grenoble, France2KTH Stockholm, Department of Applied Physics, SE-114, 128 Stockholm, Sweden3Univ. Grenoble-Alpes, CNRS-Institut Néel, 25 av. des Martyrs, F-38000 Grenoble, France4Univ. Grenoble-Alpes, CEA-INAC-MEM, 17 av. des Martyrs, F-38000 Grenoble, France

E-mail: eva.monroy@cea.fr

Received 9 October 2018, revised 4 December 2018Accepted for publication 14 December 2018Published 7 February 2019

AbstractIn this paper, we study the impact of using III-nitride semiconductors (GaN, AlN) as substratesfor ultrathin (11 nm) superconducting films of NbTiN deposited by reactive magnetronsputtering. The resulting NbTiN layers are (111)-oriented, fully relaxed, and they keep anepitaxial relation with the substrate. The higher critical superconducting temperature(Tc=11.8 K) was obtained on AlN-on-sapphire, which was the substrate with smaller latticemismatch with NbTiN. We attribute this improvement to a reduction of the NbTiN roughness,which appears associated with the relaxation of the lattice misfit with the substrate. On AlN-on-sapphire, superconducting nanowire single photon detectors were fabricated and tested,obtaining external quantum efficiencies that are in excellent agreement with theoreticalcalculations.

Keywords: NbTiN, superconductor, GaN, AlN, single photon detector

(Some figures may appear in colour only in the online journal)

1. Introduction

Superconducting ultrathin (few-nm size) films are the key-stone of devices such as superconducting hot electron bol-ometer mixers [1–4] or superconducting nanowire singlephoton detectors (SNSPDs) [5–9]. Furthermore, the integra-tion of such superconducting layers in semiconductor struc-tures has been explored as an approach to improve theperformance and add new features to high electron mobilitytransistors [10], and could grant access to interesting physicalphenomena involving Majorana fermions [11] and topologi-cal insulators [12]. Niobium titanium nitride (NbTiN) iswidely used in applications requiring nm-size films due to itsphysical and chemical stability. In comparison with NbN,NbTiN devices have demonstrated higher optical quantumefficiency, smaller recovery time, and reduced noise [13, 14].The origin of these improvements remains partially unclear,though it is generally attributed to a better crystalline quality,lower atomic concentration of oxygen, and higher metallic

conductivity, which results in lower kinetic induc-tance [13, 15].

The deposition of crystalline Nb(Ti)N materials bymolecular-beam epitaxy [10] or chemical vapor deposition[16] requires relatively high substrate temperatures (≈800 °Cand 900 °C–1300 °C, respectively). Therefore, compatibilitywith device processing imposes the deposition by sputtering,where polycrystalline ultrathin films with excellent morph-ology can be obtained in the temperature range of 25 °C–300 °C [17–19]. However, the superconducting performanceof NbTiN layers, namely the critical temperature at which thephase transition from resistive to superconducting stateoccurs, depends on the layer thickness and its structuralquality.

The most stable crystalline configuration of NbTiN is therock-salt cubic structure, with a lattice parameter betweenaNbN=4.39 Å [17] and aTiN=4.24 Å [20]. The use of III-nitride semiconductors (GaN, AlN) as substrates for NbTiN isinteresting because the equivalent lattice constant of NbN in

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the (111) plane a 3.104NbN111 =( ) Å is closely lattice matched to

the in-plane lattice constant of wurtzite AlN (aAlN =3.112 Å,mismatch<1%) and GaN (aGaN =3.189 Å, mis-match≈3.5%). These III-N materials present the additionalinterest of being optically transparent in a large spectral range,from their band gap (200 nm and 365 nm for AlN and GaN,respectively) to the far infrared, with the exception of the9.6–19 and 7.3–9 μm regions that correspond to the first andsecond harmonics of the reststrahlen band [21, 22].

It has been reported that the use of crystalline GaN,AlGaN or AlN as substrates results in an improvement of thecrystalline quality and critical superconducting temperature ofNb(Ti)N thin films, which grow epitaxially on (0001)-orien-ted III-N [16–18, 23]. However, there is almost no informa-tion on the performance of SNSPDs fabricated on III-nitrides.In a conference contribution, Zhu et al showed NbN SNSPDson crystalline AlN-on-sapphire with reduced jitter but poordetection efficiency (<4%) [24]. On the other hand, the use ofsputtered (polycrystalline) AlN as a buffer layer for thedeposition of NbN on GaAs substrates resulted in improvedperformance of SNSPDs in comparison with detectors fabri-cated on bare GaAs [25]. However, the efficiency of suchdevices was only 5% at 900 nm. It increased up to 31% at385 nm, but the substrate absorption at that wavelength wouldprevent the implementation of the microcavity or waveguidebased designs required to get close-to-unity efficiencies [26].

In this paper, we study the impact of the substrate on thecrystalline quality and superconducting critical temperature ofultrathin (11 nm) films of NbTiN deposited on almost-lattice-matched III-nitride semiconductors by reactive magnetronsputtering. Various materials are considered as substrates,namely a 1 μm thick AlN-on-sapphire template, a GaN/AlN(650 nm/1 μm) heterostructure on sapphire, and 350 μmthick GaN substrates, either non-intentionally doped (n-typeconductive) or Fe-doped (semi-insulating).

2. Methods

Thin (≈11 nm) NbTiN films were deposited by reactivemagnetron co-sputtering at room temperature in an ultra-highvacuum chamber (background pressure between 5×10−9

Torr and 1×10−8 Torr). After solvent cleaning (acetone,methanol), the substrates were placed on a 4″ wafer chuck andheld in place using aluminum pins. During the deposition, thesubstrate holder was rotating in order to improve the radialuniformity of the samples. The substrates were held at adistance of about 30 cm from the targets. The Nb target wasplaced directly below the substrate holder, while the Ti targetwas placed in a confocal geometry, the target pointingtowards the substrate holder. Both targets were 3″ in diameterand 0.250″ thick. The applied power on the Nb target was200W (direct current), while the applied power on the Titarget was 200W (radiofrequency), which corresponds to apower density of 4.39W cm−2. The sputtering pressure wasset to 3 mTorr with a gas mixture of 100 sccm of Ar and 10sccm of N2. A quartz crystal monitor was calibrated bydeposition of a thick film and subsequent measurement of the

deposited thickness with a profilometer. From measurementson previous samples deposited in the same conditions, weestimate the thickness variation in 1 ×1 cm, to be less than1%. The estimated deposition rate was 0.1 nm s−1. Thesamples were deposited two at a time during subsequent runs,and under similar conditions, namely same pressure, gaspartial pressures, applied powers, plasma voltage and current.The nominal Ti mole fraction in the Nb1−xTixN layer wasx=0.2, but chemical measurements by electron energy lossspectroscopy and energy-dispersive x-ray spectroscopy ofreference specimens, performed in a transmission electronmicroscope, point to x=0.15±0.03. Substrates con-sisted of:

(i) a commercial template (AlN-on-sapphire template)consisting of 1 μm thick (0001)-oriented AlN depositedby metalorganic vapor phase epitaxy (MOVPE) onc-plane sapphire (sample SA);

(ii) a 650 nm-thick (0001)-oriented GaN layer deposited byplasma-assisted molecular-beam epitaxy (PAMBE) on acommercial template consisting of 1 μm thick AlNdeposited by MOVPE on c-plane sapphire (sam-ple SAG);

(iii) a 350 μm thick (0001)-oriented GaN substrate (sampleSG) diced from thick GaN boules grown by hydridevapor phase epitaxy on c-plane sapphire; and

(iv) a 350 μm thick (0001)-oriented semi-insulating Fe-doped GaN substrate (sample SGF) diced from thickFe-doped GaN boules grown by hydride vapor phaseepitaxy on c-plane sapphire.

Prior to the deposition, the surface was treated in situwith a 25W radiofrequency Ar plasma for 10 s. The samplesunder study are listed in table 1.

X-ray reflectivity and x-ray diffraction measurements(XRD) were performed in a Panalytical Empyrean dif-fractometer equipped with a cobalt anode beam tube (CoλΚα=1.789 Å), a Göbel mirror and a two-dimensional pixeldetector used in both zero-dimensional and one-dimensionalmodes.

The microstructure of the samples was analyzed by high-resolution transmission electron microscopy (HRTEM). Thesamples were prepared in cross-section by either mechanicalpolishing followed by ion milling or by focused ion beammilling and measured in a FEI-Tecnai microscope operated at200 kV. Finally, the surface morphology was measured byatomic force microscopy (AFM) in a Dimension 3100 systemoperated in the tapping mode.

3. Results and discussion

3.1. Material characterization

The thickness of the NbTiN layer has been determined pre-cisely using x-ray reflectivity. Examples of these measure-ments corresponding to samples SA and SGF are illustrated infigure 1, together with fits using the GenX software [27]. For

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Supercond. Sci. Technol. 32 (2019) 035008 H Machhadani et al

all the samples, the fit confirms total layer thickness around11 nm (see precise values and error bars in table 1). Getting agood agreement with the experimental results requiresassuming a multilayer structure consisting of a bottomNb0.8Ti0.2N layer (≈8.45±0.45 nm) capped by anNb0.8Ti0.2N0.9O0.1 layer (≈2.1±0.2 nm) and by a mixture ofNb2O5 and TiO2 (less than one atomic layer, with(Nb2O5)0.7(TiO2)0.3 composition). Post-growth oxidation andNb2O5 and TiO2 demixing are known to occur in NbTiN thinfilms, but experiments as a function of time show a saturationso that it remains a surface phenomenon [28]. Furthermore,due to the hydrophilic nature of the material, a furtherimprovement of the fit is observed when assuming the pre-sence of a layer of H2O at the surface (see figure 1). Thevalues of root-mean-square (RMS) roughness of the topmostlayer extracted from the calculations are also summarized intable 1, considering the fits with and without watertermination.

To identify the crystalline orientation of the NbTiN filmand its epitaxial relationship with the substrates, structuralstudies were performed by HRTEM along both [11–20] and[10–10] zone axis of the III-nitride substrates. Figure 2(a)show sample SAG viewed along the [11–20] zone axis ofGaN. The superconducting film grows along the [111] axis,and it contains twin domains that are rotated by 60°. Theimages confirm the nominal crystallographic orientation ofthe substrates, and the establishment of NbTiN(111) [2–1–1]|| (Al,Ga)N (0001) [10–10] and NbTiN(111) [2–1–1] || (Al,Ga)N(0001) [01–10] epitaxial relationships, as previouslyobserved in the case of NbN layers [10, 18, 23]. The presenceof dislocations at the interface is consistent with the relaxationof the misfit (36 GaN planes correspond to 37 NbTiN planes,as illustrated in figure 2(b)). In the case of SGF, observed inthe same orientation, the thin film presents the same structural

characteristics, but a strong contrast is observed at theNbTiN/GaN:Fe interface (arrow in figure 2(c)). This contrasthas been assigned to the segregation of Fe [29, 30], which isused as a dopant to render the GaN insulating. Finally,figure 2(d) depicts the NbTiN/AlN interface in sample SA,viewed along the [10–10] zone axis of AlN. The interfacepresents an epitaxial relationship as observed for NbTiN onGaN, but with lower density of dislocations, which appearseparated by more than 100 AlN m planes. This is consistentwith the NbTiN lattice being more closely matched to AlNthan to GaN.

The variation of the resistance with temperature for thesamples under study is presented in figure 3. The super-conducting critical temperature moves in the range fromTc=10.6 to 11.8 K, depending on the substrate, with asuperconducting transition range (over which the resistancevaries from 90% to 10% of its maximum value)ΔT=0.83–0.86 K. Precise values of Tc and ΔT for thesamples under study are summarized in table 1, and theyrepresent a significant improvement in comparison with ourtypical results of similar NbTiN layers deposited on drythermal SiO2 on Si, whose Tc is in the range of 9.8±0.3 Kwith ΔT≈0.87. A similar enhancement of Tc was observedby Shiino et al when inserting a sputtered AlN buffer layerbetween the NbTiN thin film and the quartz substrate [17].This improvement is attributed to the good lattice matchingbetween (111)-oriented rock-salt NbTiN and (0001)-orientedwurtzite AlN.

The superconducting properties of NbTiN might dependon its strain state [31]. In this sense, Makise et al showed anincrease of Tc in NbTiN ultrathin films with a moderate ten-sile strain (out-of-the-plane lattice constant a⊥ around4.35–4.39 Å in layers with a relatively high Ti content,around 30%) grown on various substrates. Krause et al reporta degradation of the superconducting properties of NbN whenincreasing the Al content of AlGaN substrates from GaNtowards AlN [17], which implies reducing the lattice mis-match with the substrate. However, the possible correlation ofthis trend with the strain in the layers was not analyzed. In ourcase, if we look at the in-plane lattice parameter of the sub-strate listed in table 1 (results extracted from XRD measure-ments of the (0002) reflection of AlN or GaN, assumingbiaxial strain), we see that it evolves from aAlN (SA) to aGaN(SG, SGF), passing through an intermediate state witha=3.170 Å due to the partial relaxation of the thin GaNlayer on AlN for sample SAG. This slow relaxation is char-acteristic of III-nitride films grown by PAMBE under metal-rich conditions [32]. If we compare the evolution of Tc withthe lattice parameter of the substrate (both listed in table 1),we observe an increase of Tc for decreasing substrate latticeparameter, i.e. a systematic improvement of the super-conducting properties as we reduce the lattice mismatchbetween NbTiN and the substrate.

To get a precise assessment of the strain state of thesuperconducting layer, a detailed XRD study was conducted.The (111) inter-planar distance of the NbTiN layers along the[111] growth axis (d[111]) was extracted from the angularposition of the (111) and (222) reflections in ω–2θ scans,

Figure 1. X-ray reflectivity of (a) the NbTiN film on AlN-on-sapphire (sample SA), and (b) the NbTiN film on GaN:Fe (sampleSGF). Grey squares are experimental measurements and the solidlines are fits generated with the GenX software. Note that in the caseof SA, fits with and without H2O wetting layer are almostsuperimposed.

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whereas the inter-planar distance along the in-plane [2–1–1]axis (d[2−1−1]) was extracted from the angular position of the(311), (133), (224), and (511) reflections. Average values ofd[111] and d[2−1−1] are presented in table 1. From such values,we can calculate the equivalent out-of-the-plane and in-planelattice parameters, a⊥ 3= d[111] and a|| 6= d[2−1−1],respectively, also presented in the table. For all the samples,a⊥ and a|| are identical, within the error bars of the mea-surements, which means that the samples are fully relaxed.

Figure 4 compares the surface morphology of the NbTiNlayers under study, measured by AFM in the tapping mode.Typical AFM images shown in figures 4(a) and (b)(describing samples SA and SGF, respectively) show thingrainy layers. The surface roughness presents significantdifferences from sample to sample, as summarized infigure 4(c). Comparing samples SA and SGF, the averageheight increases from 1.9 to 4.7 nm, while the RMS rough-ness evolves from 0.85 to 1.6 nm, respectively. Note thatthese values are higher than the surface roughness of thesubstrates (shown in table 1), and there is no correlationbetween the NbTiN roughness and the substrate roughness.On the contrary, the variation of the NbTiN roughness fromsample to sample correlates well with the lattice mismatchbetween the superconducting film and the substrate, whichconfirms that the strain relaxation plays a role in the surfaceroughness development. Let us remind that for low misfitsand ultrathin layers, relaxation can be achieved by elasticundulation of the surface prior to the formation of disloca-tions [33].

From the structural analysis of the NbTiN layers weconclude that there is an enhancement of Tc in epitaxial layersgrown on III-nitrides with respect to layers deposited on

amorphous materials, like SiO2. A further improvement isobserved as the substrate gets more closely lattice matched tothe NbTiN epilayer, i.e. the Tc is higher for material depositedon AlN with respect to deposition on GaN. This trend cannotbe related to the strain state, since the samples are fullyrelaxed. We therefore attribute it to the reduced roughness ofthe NbTiN film. This result might also explain the resultsobserved by Krause et al when depositing NbN on variousAlxGa1−xN, buffer layers [23], who showed a decrease of Tcfor increasing Al mole fraction. In absence of studies of thestrain state of the superconductor, an enhancement of theroughness in the ternary alloys could explain the degradationof the superconducting performance.

3.2. Fabrication and characterization of SNSPDs

In order to assess the suitability of such NbTiN films to theforeseen application, we have fabricated SNSPDs fromsample SA, which displayed the best superconducting prop-erties. The devices were designed for operation under normalincidence illumination. The NbTiN film was patterned into ameander structure as described in [8], using e-beam litho-graphy and inductively-coupled plasma etching. The diameterof the detector area was 15 μm. The nanowire width was70 nm, with a pitch of 150 nm, as illustrated by the scanningelectron microscopy (SEM) image in the insert of figure 5(a).

We used a dip-stick system to immerse the detector inliquid helium. In our system, the detectors and the internalelectronics are immersed within liquid helium, ensuring astable operation temperature of 4.2 K. Continuous-wave laserdiodes emitting at wavelengths λ=1.31 and 0.65 μm wereused for optical excitation. The laser power was attenuated in

Table 1. Structural and electrical properties of the samples under study: nature of the substrate; substrate lattice parameter (aSubs); thickness ofNbTiN and total thin film thickness extracted from x-ray reflectivity (XRR), together with the root-mean-square (RMS) topmost surfaceroughness assumed for the fit, without and with water termination; out-of-the-plane and in-plane lattice parameters of NbTiN measured fromXRD (d[111] and d[2-1-1], respectively) together with the cubic lattice parameters calculated from d[111] and d[2-1-1] assuming a regular cubiclattice (a⊥ and a||, respectively); average peak height and RMS roughness extracted from AFM measurements of the NbTiN samples and ofthe substrates; from resistance versus temperature measurements (R(T)), critical superconducting temperature (Tc) and temperature range ofsuperconducting switching (ΔT) taken as the difference between the temperatures corresponding to a resistance drop of 10% and 90% fromthe maximum value.

Sample SA SAG SG SGF

Substrate Sapphire/AlN Sapphire/AlN/GaN GaN GaN:FeaSubs (Å) 3.112 3.170 3.189 3.189

XRR NbTiN thickness (nm) 8.7±0.1 8.3±0.1 8.9±0.6 7.9±1.0Total thickness (nm) 11.0±1.4 10.9±0.3 11.3±0.5 10.8±0.5RMS roughness (nm) 3.5 1.5 0.8 2.0RMS roughness with H2O (nm) 0.5 0.6 1.1 1.8

XRD d[111] (Å) 2.538±0.003 2.536±0.003 2.538±0.003 2.536±0.004d[2-1-1] (Å) 1.797±0.010 1.791±0.005 1.798±0.004 1.791±0.005a⊥ (Å) 4.396±0.006 4.393±0.006 4.396±0.006 4.393±0.008a|| (Å) 4.402±0.010 4.386±0.008 4.403±0.006 4.386±0.008

AFM average peak height sample (nm) 1.9 2.3 3.8 4.7RMS roughness sample (nm) 0.85 0.85 1.5 1.6average peak height substrate (nm) 1.3 2.0 1.0 1.0RMS roughnes substrate (nm) 0.15 0.5 0.11 0.11

R(T) Tc (K) 11.8 11.3 11.0 10.6ΔT (K) 0.83 0.85 0.86 0.85

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order to obtain a photon flux around 106 photon s−1.Figures 5(a) and (b) show the evolution of the detectionefficiency at λ=1.31 μm and 0.65 μm, respectively, as afunction of the bias current/critical current ratio (Ib/Icr). Thedark count rate is superimposed on figure 5(a). As expected[34], the efficiency is maximum for transverse-electric (TE)polarization, where the electric field oscillates along thenanowire length, and drops down for transverse-magnetic

(TM) polarized light, where the electric field oscillates alongthe nanowire width. At λ=1.31 μm, the highest efficiencyrecorded was 21% for TE polarization, but the response is notfully saturated. On the contrary, at λ=0.65 μm, the higherphoton energy results in full saturation for Ib/Icr≈0.8at 4.2 K.

Note that the devices present a very low level of darkcounts, about ten times lower than typical measurements inSNSPDs on SiO2/Si substrates. The low dark count rate isexplained by the high critical current (35±3 μA, whichcorresponds to a critical current density in the meander of≈5.9 MA cm−2). Therefore, the voltage trigger level is wellabove the noise level of the readout system, which reduces theprobability of dark counts. The enhancement of the criticalcurrent (and reduction of the noise level) is consistent with the

Figure 2. (a), (b) HRTEM images of the NbTiN layer and theNbTiN/GaN interface of sample SAG viewed along the [11–20]zone axis of GaN. (c) HRTEM image of SGF viewed along the[11–20] zone axis of GaN. The arrow marks the contrast at theNbTiN/GaN:Fe interface. (d) HRTEM image of the NbTiN/AlNinterface in sample SA, viewed along the [10–10] zone axis of AlN.

Figure 3. Variation of the resistance of the NbTiN layers under studyas a function of temperature. The curve for an NbTiN deposited ondry thermal SiO2 on Si under identical conditions was added forcomparison. The resistance of the various samples was normalized toits maximum value.

Figure 4.Atomic force microscopy images of samples (a) SA and (b)SGF. (c) Representation of the average height and RMS roughnessextracted from 800×800 nm2 AFM images of samples SA, SAG,SG and SGF.

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improvement observed by Schmidt et al when inserting asputtered AlN buffer layer before the deposition of NbN onGaAs [25].

The device performance is modeled using finite-differ-ence time-domain (FDTD) calculations with the commercialRSoft FullWave software [26, 34]. The meander is modeledas a single grating period with in-plane boundary periodicconditions, as described in the inset of figure 5(c). Calcula-tions assume an 8.5 nm-thick NbTiN active wire with a widthof 70 nm and a pitch of 150 nm. The absorption efficiency iscalculated from the difference between the input power andthe reflected plus transmitted power, once the steady state isreached. The refractive indices used as input parameters were4.17+i5.63 and 2.08+i2.95 for NbTiN at 1.31 μm and0.65 μm, respectively, 1.74 for sapphire, and 2.15 for AlN.

Figures 5(c) and (d) present the simulated absorptionefficiency of the NbTiN wire at λ=1.31 and 0.65 μm, forTE and TM polarization, as a function of the thickness of theAlN template. The oscillatory patterns are due to Fabry–Perotinterference in the AlN layer. The experimental values arerepresented with error bars that illustrate the uncertainty on

the thickness of the AlN layer and the dispersion of efficiencyvalues for several devices. At λ=1.31 μm, the measure-ments approach the theoretical results, in spite of the fact thatthe experimental efficiency curves are not fully saturated. Onthe contrary, at λ=0.65 μm, full saturation is reached,leading to an excellent fit between the experimental resultsand the simulations, which implies that the internal quantumefficiency is close to one. Therefore, these experiments can beconsidered as a validation of the approach from material pointof view. Then, an enhancement of the external efficiency canbe easily obtained by modifying the nitride layer thickness tocreate a microcavity operating at the desired wavelength, orby implementing a GaN waveguide, if the aim is broadbandoperation (note that the SAG sample has already the adequatelayer sequence for waveguide fabrication) [26].

4. Conclusion

In conclusion, we studied superconducting and structuralproperties of ultrathin layers of NbTiN sputtered on III-nitride

Figure 5. (a) Detection efficiency as a function of the bias current/critical current ratio (Ib/Icr), measured for an SNSPD device fabricated onsample SA and measured at 1.31 μm and at 4.2 K (liquid He immersion). The dark count rate is also represented. Inset: SEM image of adetail of the superconducting nanowire meander. (b) Detection efficiency as a function of Ib/Icr, measured at 0.65 μm and at 4.2 K. The darkcount rate is also represented. (c) Calculated dependence of TE and TM absorption efficiency at 1.31 μm as a function of the thickness of theAlN layer. Experimental results are presented as squares with their associated error bars. Inset: scheme of the structure for which simulationshave been performed. (d) Calculated dependence of TE and TM absorption efficiency at 0.65 μm as a function of the thickness of the AlNlayer. Experimental results are presented as squares with their associated error bars.

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semiconductor substrates. The NbTiN films grow along the[111] axis, and they keep an epitaxial relation with thewurtzite substrate. The superconducting critical temperature isin the range of Tc=10.6–11.8 K, depending on the substrate,with a sharp superconducting transition (ΔT=0.83–0.86 K).This represents an improvement with respect to layersdeposited on amorphous substrates, like dry thermal SiO2

(Tc=9.8±0.3 K, ΔT≈0.87). Higher Tc with smaller ΔTis obtained for deposition on AlN, whose crystalline lattice isbetter matched to NbTiN than that of GaN. The improvementwith respect to GaN-based substrates is not related to thestrain state, since all the NbTiN layers are fully relaxed.Instead, we attribute the higher Tc to a reduction of the NbTiNroughness when deposited on a lattice matched substrate.Based on these results, we have demonstrated the firstsuperconducting nanowire single photon detectors on crys-talline AlN, showing external quantum efficiencies that fitwell with theoretical calculations.

Acknowledgments

The authors acknowledge financial support from the FrenchNational Research Agency via the ‘WASI’ (ANR-14-CE26-0007) program, and from the Grenoble Nanoscience Foun-dation via the ‘NAQUOP’ project.

ORCID iDs

Jean-Michel Gérard https://orcid.org/0000-0002-0929-0409Eva Monroy https://orcid.org/0000-0001-5481-3267

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